How can I model this twisted arrangement of cubes?
Particles or Manual Edit

Consider using a Particle System on a helix strip mesh created by Simple Deform Twist modifier.  Particles would be a group of objects which are cubes with random variation of shape.  Use Initial Orientation Normal with some small Random Value as depicted above.  No Array Modifier.

If you have just a few cubes you could
Press the [Convert] button to make duplicates real
and give each a rotation by hand.

The imperfect cubes are in a group and you can see a rotation of one in edit mode.

You may wish to state if you want to keep the varIations in cube shape and rotation.





The image above show 2 examples of orientation.

Full Coverage.  Placing a single particle on each face in the Helix Mesh.



[Emission Number] = (face count + 1). Goal 1 particle per face. Close to meeting goal. Result is 2 particles in same position on top. I have never investigated if this is declared a defect. (I have never investigated fully.) If you are going to [Convert make real] this problem may lessen, since you can delete. [Particles/Face=1].  A Hidden Portion of curve may be a bearable near solution.  You can see the two different colored particles on top.  When you increment and decrement Emission Number you can see this (interesting) situation.